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We consider the problem of tensor estimation from noisy observations with possibly missing entries. A nonparametric approach to tensor completion is developed based on a new model which we coin as sign representable tensors. The model…
In CS literature, the efforts can be divided into two groups: finding a measurement matrix that preserves the compressed information at the maximum level, and finding a reconstruction algorithm for the compressed information. In the…
This paper proposes a novel formulation of the tensor completion problem to impute missing entries of data represented by tensors. The formulation is introduced in terms of tensor train (TT) rank which can effectively capture global…
In this paper, we briefly discuss the dynamic and functional approach to computer symbolic tensor analysis. The ccgrg package for Wolfram Language/Mathematica is used to illustrate this approach. Some examples of applications are attached.
A parameterization is described for quantifying translational motion of a point in three-dimensional Euclidean space. The parameterization is similar to well-known parameterizations such as spherical coordinates in that both position and…
In this work, the Einstein notation is utilized to synthesize state and parameter transition matrices, by solving a set of ordinary differential equations. Additionally, for the system identification problem, it has been demonstrated that…
Here we generalize the concept of spatial tensor product, introduced by Skeide, of two product systems via a pair of normalized units. This new notion is called amalgamated tensor product of product systems, and now the amalgamation can be…
The Invar package is introduced, a fast manipulator of generic scalar polynomial expressions formed from the Riemann tensor of a four-dimensional metric-compatible connection. The package can maximally simplify any polynomial containing…
Tensor train (TT) format is a common approach for computationally efficient work with multidimensional arrays, vectors, matrices, and discretized functions in a wide range of applications, including computational mathematics and machine…
The tensor notation used in several areas of mathematics is a useful one, but it is not widely available to the functional programming community. In a practical sense, the (embedded) domain-specific languages (DSLs) that are currently in…
High-dimensional data arise naturally in many areas of science and engineering, including machine learning, signal processing, computational physics, and statistics. Such data are often represented as tensors, multi-dimensional…
Classical tensors, the familiar mathematical objects denoted by symbols such as $t_{i}$, $t^{ij}$ and $t_{k}^{ij}$, are usually interpreted either as 'coordinatizable objects' with coordinates changing in a specific way under a change of…
We introduce a tensor-based model of shared representation for meta-learning from a diverse set of tasks. Prior works on learning linear representations for meta-learning assume that there is a common shared representation across different…
We present an incremental, scalable and efficient dimension reduction technique for tensors that is based on sparse random linear coding. Data is stored in a compactified representation with fixed size, which makes memory requirements low…
Kjolstad et. al. proposed a tensor algebra compiler. It takes expressions that define a tensor element-wise, such as $f_{ij}(a,b,c,d) = \exp\left[-\sum_{k=0}^4 \left((a_{ik}+b_{jk})^2\, c_{ii} + d_{i+k}^3 \right) \right]$, and generates the…
Statistical inference for tensors has emerged as a critical challenge in analyzing high-dimensional data in modern data science. This paper introduces a unified framework for inferring general and low-Tucker-rank linear functionals of…
Tensor network diagram (graphical notation) is a useful tool that graphically represents multiplications between multiple tensors using nodes and edges. Using the graphical notation, complex multiplications between tensors can be described…
In this paper, we extend the analysis of random Kronecker graphs to multi-dimensional networks represented as tensors, enabling a more detailed and nuanced understanding of complex network structures. We decompose the adjacency tensor of…
The widespread use of multi-sensor technology and the emergence of big datasets has highlighted the limitations of standard flat-view matrix models and the necessity to move towards more versatile data analysis tools. We show that…
Tensor regression has attracted significant attention in statistical research. This study tackles the challenge of handling covariates with smooth varying structures. We introduce a novel framework, termed functional tensor regression,…